(B) function $f(x)$ is increasing if $f'(x) > 0$.Given $f(x) = x^3 - 27x + 5$.Differentiating with respect to $x$,we get $f'(x) = 3x^2 - 27$.For the f

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(B) function $f(x)$ is increasing if $f'(x) > 0$.Given $f(x) = x^3 - 27x + 5$.Differentiating with respect to $x$,we get $f'(x) = 3x^2 - 27$.For the function to be increasing,we set $f'(x) > 0$:$3x^2 - 27 > 0$$3(x^2 - 9) > 0$$x^2 - 9 > 0$$x^2 > 9$Taking the square root on both sides,we get $|x| > 3$.Thus,the function is increasing when $|x| > 3$.

Class 12 Mathematics Applications of Derivatives Increasing and Decreasing function

Easy

$f(x) = x^3 - 27x + 5$ is an increasing function,when

A
$x < -3$
B
$|x| > 3$
C
$x \le -3$
D
$|x| < 3$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Mathematics Questions

Chapter

Applications of Derivatives

Subtopic

Increasing and Decreasing function

The interval in which the function $f(x) = x^x, x > 0$,is strictly increasing is

MediumJEE MAIN 2024

View Solution

For what values of $x$ is the function $f(x) = 2x^3 - 9x^2 + 12x + 29$ decreasing?

Difficult

View Solution

What type of function is $y = x^4$?

Medium

View Solution

Let $R^* = R - \left\{ (2k - 1) \frac{\pi}{2} \mid k \in I \right\}$. The function $f: R^* \rightarrow R$ is defined as $f(x) = \tan x - x$, then $f(x)$ is

EasyTS EAMCET 2021

View Solution

If $f(x) = x^3 - 6x^2 + 9x + 3$ is a monotonically decreasing function,then $x$ lies in:

EasyMHT CET 2024

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

$f(x) = x^3 - 27x + 5$ is an increasing function,when

Similar Questions

The interval in which the function $f(x) = x^x, x > 0$,is strictly increasing is

For what values of $x$ is the function $f(x) = 2x^3 - 9x^2 + 12x + 29$ decreasing?

What type of function is $y = x^4$?

Let $R^* = R - \left\{ (2k - 1) \frac{\pi}{2} \mid k \in I \right\}$. The function $f: R^* \rightarrow R$ is defined as $f(x) = \tan x - x$, then $f(x)$ is

If $f(x) = x^3 - 6x^2 + 9x + 3$ is a monotonically decreasing function,then $x$ lies in:

Vedclass Test Series

Exam Paper Generator

Online Exam Module